There are certain ideas in Indian-Jaina logic called syadvada
which seem to have close relevance to the concepts of
probability, and which can, therefore supply a convenient
background to my own observations on the foundations of
statistics. It is always difficult to be sure about the exact
meaning of logical and philosophical phrases which were current
1500 or 2500 years ago : and it is not claimed (and I also agree
that it would not be correct to claim) that the concept of
probability in its present from was recognised in syadvada but
the phrases used in syadvada seem to have a special significance
in connection with the logic of statistical inference.

I shall first give a brief historical account of syadvada.
Jaina religion and philosophy came into prominence from the time
of its great leader Mahavira (599-527 B.C.) who was a
contemporary of Buddha, the founder of the Buddhist religion. The
earliest reference to syadvada occurs is the writings of
Bhadrabahu who is believed to have given the following
explanation of syadvada : syat = "may be", and vada =
"assertion", or the assertion of possibilities.1

"The syadvada is set forth as follows : (1) May be, it
is; (2) may be, it is not; (3) may be, it is and it is not; (4)
may be, it is indescribable; (5) may be, it is and yet is
indescribable; (6) may be, it is not and it is also
indescribable; (7) may be, it is and it is not and it is also
indescribable."2

There were two authors of the name Bhadrabahu, the senior
belonging to the period 433-357 B.C., and the junior to about 375
A.D., and it is not definitely known whether the above
explanation was given by the senior or the junior Bhadrabahu; but
the above exposition is usually ascribed to the senior Bhadrabahu
of the 4th century B.C.1 There is indisputable mention
of syadvada in the Nyayavatara of Siddhasens Divakara2
(about 480-550 A.D.). A little later Samantabhadra (about 600
A.D.) gives a full exposition of the seven parts of Syad-vada or
Sapta-bhanginaya in his Aptaminamsa.3 It is clear that
syadvada was well developed by the sixth century A.D.,and
received a great deal of attention in the mediaeval period of
Indian logic; the syadvadamanjari of Mallisena (1292 A.D.) for
example, is a separate treatise on `the same theory.4
There are, of course, still later works such as Vimala Dasa's
Saptabhangitarangini and a large number of mediaeval and modern
commentaries. I am, therefore, dealing with a well-known theme
which is considered to be the most original contribution of Jaina
logic to Indian thought.5

Dialectic of Seven-fold
Predication

I shall next refer to the actual text in Sanskrit of the
dialectic of sevenfold predication (saptabhanginaya) :

(1) syndasti 6 = may be, it is.

(2) syatnasti = may be, it is not.

(3) syadasti nasti 7ca = may be, it
is, it is not.

(4) syadavaktavyah8 = may be, it is indeterminate.

(5) syadasti ca9 avaktavya sca10 = may
be, it is and also indeterminate.

(6) syatnasti ca avaktavyasca = may be, it is not and also
indeterminate.

(7) syadasti nasti ca avaktav-yasca = may be, it is and it is
not and also indeterminate.

The word syat has been translated as "may be" but
this does not bring out the full implications. The Sanskrit word
in mentioning one possibility has also some indirect allusion to
other possibilities. The Sanskrit word asti may be rendered as
"it is", "it exists", or "it is
existent"; and nasti is the negation, i.e. "it is
not" "it does not exist", or "it is
non-existent". The third category predicates the possibility
of both asti and nasti; of both "it is" and "it is
not". The first three categories conform thus to the
categories of classical logic and do not present any difficulty.

The fourth category is avaktavya which I have translated as
"indeterminate". Other authors have used the words
"indescribable", or "inexpressible" or
"indefinite". For example, Satkari Mookerjee explains
"The inexpressible may be called indefinite".... (JPN,
p. 115). I prefer "indeterminate" because this is
nearer the interpretation which I have in mind.

It will be useful if at this stage I give an illustration.
Consider the tossing of a coin; and suppose it turns up
"head". We may then say (1) "it is head"
(now). This also implies, (2) "it is not-head" (on some
other occasion). The third category follows without difficulty,
(3) "it is, and it is not" which is a synthetic
predication based on both (1) and (2). The fourth category
predicates that the position is still (4) indeterminate.

This, however, does not exhaust the possibilities of
predication or modes of knowledge. For example, if we know that
it is a coin which has "head" on one side and
"not-head" or "tail" on the other side, and
we also know that it must turn up either "head" or
"tail", we may then predicate that (5) there exists one
type of indeterminateness which is capable of being resolved in
terms of the first four categories. On the other hand we may know
that the subject of discourse is not a coin but something else to
which the category of indetermination in the above sense cannot
apply, we may then use the sixth mode of predication and assert
that (6) there does not exist that type of indeterminateness
which is capable of being resolved in terms of the first four
categories. Finally, there is the seventh mode of knowledge where
we may be able to predicate that sometimes the possibility of
resolution of indetermination exists (as in the fifth mode) and
sometimes this possibility does not exist (as in the sixth mode).

According to syadvada, the above seven categories are
necessary and are also sufficient so that they exhaust the
possibilities of knowledge. There is a minority view which hold
that there are further possibilities of (8) vaktavyasca
avaktavyasca, a kind of duplicated indeterminateness together
with successive categories of the fifth, sixth, and seventh types
in an infinite regression but the accepted opinion is that the
hypothetical eighth category is identical with the fourth so that
there is no need of more than seven categories.

I should like to emphasise that the fourth category is a
synthesis of three basic modes of "it is" (assertion)
"it is not" (negation), and inexpressible, or
indefinite, or "indeterminate" (which itself is
resolvable into either "it is" or "it is
not"), and supplies the logical foundations of the modern
concept of probability. Consider the throw of a coin. It has the
possibility of head (it is) or not-head (it is not); sometimes
head and sometimes not head; and the combination of both
possibilities of "it is" and "it is not" in
an yet indefinite or indeterminate form. The fifth category of
knowledge in Jaina logic predicates the existence of
indetermination (which we may perhaps interpret, in modern
language, as the assertion of the existence of a probability
field). The sixth category denies the existence of a probability
field; while the seventh category covers the whole range of
possibilities mentioned in the other six categories.

Relativism

It would be of interest to consider some further aspects of
Jaina logic. The points to be stressed are that Jaina thought is
non-absolutist (that is, it is relativist) and realist.
Siddhasena Divakara (480-550 A. D.) in Nyayavatara (which is
accepted as the earliest Jaina work on pure logic at present
available) gave an exposition of syadvada (knowledge of the
all-sided method) of which the authentic text is described below
:

"Syadvada, which literally signifies assertion of
possibilities, seeks to ascertain the meaning of things from all
possible standpoints. Things are neither existent nor
non-existent absolutely .... Syad which signifies "may
be" denotes all these seven possibilities, that is, a thing
may be looked at from one of the above seven points of view,
there being no eighth alternative."1

It has been pointed out that :

"All objects are multiform (anekanta) according to him
(i.e. the Jaina). From their many-sided nature it follows that
all judgements are relative. They are true under certain
conditions. They are conditional or hypothetical. No judgements
are absolutely true. The word "perhaps" must be added
to all judgements to indicate their conditional character. This
is Syadvada or the doctrine of relativity of judgements."2

"The Jains emphasise manifold nature of real things which
are endowed with infinite qualities, modes, and relations to the
other things.2 They have identity-in-difference. The
Vedantists emphasise pure identity and deny plurality. The jainas
emphasise manifoldness of inter-related reals and deny pure
identity. They are anti-Absolutists. They are advocates of
relative pluralism."3

It has been also pointed out that :

"Thus the Jainas hold that no affirmation, or judgement,
is absolute in nature, each is true in own limited sense only,
and for each one of them any of the above seven alternatives
(technically called saptabhangi) holds good. (See syadvadamanjari
with Hemachandra's commentary p. 166 etc.) The Jainas say that
other Indian systems each from its own point of view asserts
itself to be the absolute and the only point of view. They do not
perceive that the nature of reality is such that the truth of any
assertion is merely conditional and holds good only in certain
conditions, circumstances, or senses (upadhi). It is thus
impossible to make any affirmation which is universally and
absolutely valid. For a contrary or contradictory affirmation
will always be found to hold good of any judgement in some sense
or other. As all reality is partly permanent and partly exposed
to change in the form of losing and gaining old and new
qualities, and is thus relatively permanent and changeful, so all
our affirmations regarding truth are also only relatively valid
and invalid. Being non-being and indefinite, the three categories
of logic, are all equally available in some sense or other in all
their permutations for any and every kind of judgement. There is
no universal and absolute position or negation, and all
judgements are valid only conditionally. 1

Realism

Jaina logic is essentially realistic : "The Jaina
philosopher maintains that existents are possessed of an infinite
number of attributes and characteristics which can be discovered
by experience alone. He refused to put a premium on internal
intuition. The mind, even with its active contributions, which
the Jaina does not seek to deny, is believed by him to be an
instrument of discovery and not a creator of facts." (JPN;
p.1)

"Logic has to work upon the data of experience and is as
much an instrument as experience is." "Pure logic,
prior to and independent of experience, is a blind guide to the
determination of truth. Logic is to rationalise and systematise
what experience offers. "(JPN, p.8)

" A things is existent, is non-existent and is both
existent and non-existent, but always subject to limitations
imposed by objective differences of substance, time, space and
attributes (dravya-ksetra-kala-bhavapeksaya).1 The
differences in predication are not due to our subjective
contemplation from different angles of vision, but founded upon
objectively real attributes. They are facts irrespective of the
consideration whether we contemplate them or not." (JPN,
p.107)

"The Jaina does not see any reason why things should be
particulars alone. Things are, according to the Jaina, both
universals and particulars together. A real is a particular which
possesses a generic attribute". (JPN p2.). " in
conformity with the plain verdict of experience, the nature of
reals is admitted to be made up of both the elements - universal
and the particular and to be cognised as such by perceptual
knowledge." (JPN, p.3)

"Things are neither exclusively particulars nor are they
exclusively universals, but they are a concrete realisation of
both. The two elements can be distinguished by reflective
thought, but cannot be rent asunder. So our experience of one
particular individual is not confined to that individual alone,
but extends to unperceived individuals also in so far as the
latter typify the universal as a part of their constitution.
Individuals, even when they belong to a class, will vary from one
another. Repetition of experience only helps us to take stock of
the universal in its true character, but once the latter is
known, it does not stand in verification or confirmation by
further observation".1 (JPN, p.6)

The Jaina emphasises the multiple nature of reality and
accepts the standpoint of non-absolutism. "He asserts that
neither unity nor diversity sums up the nature of a real, but
both taken together do it. Unity is not exclusive of diversity or
vice versa. The difficulty that is confronted is not grounded
upon objective reality, but arises from a subjective aberration,
which consists in the imagination of inconsistency between unity
and diversity. But unity is associated with diversity and
diversity is never found as part from unity, which is its very
foundation. (JPN, p.58)

"The central thesis of the Jaina is that there is not
only diversity of reals, but each real is equally diversified.
Diversification as induced by relations has been explained. The
conclusion is legitimate that each real is possessed of an
infinite number of modes at every moment. The number of reals is
infinite. All things are related in one way or the other and
relations induce relational qualities in the relata, which
accordingly become infinitely diversified at each moment and
throughout their career. Things are neither momentary2
nor uniform"3 . (JPN, p.70) According to the
Jaina "a real changes every moment and at the same time
continues The continuity never breaks down." (JPN, p.70)

"A real is that which not only originates, but is also
liable to cease and at the same time capable of persisting.
Existence, cessation, and persistence are the fundamental
characteristics of all that is real. This concept of reality is
the only one which can avoid the conclusion that the world of
plurality, which is the world of experience, is an
illusion." (JPN, p.72)

The relativism of the Jaina philosopher is to be sharply
contrasted with some of the other Indian systems of philosophy.

"The Vedantist start with the premise that reality is one
universal existence; the Buddhist fluxist1 believes in
atomic particulars, each absolutely different from the rest and
having nothing underlying them to bind them together. The
Naiyayika2 believes both to be combined in an
individual, though he maintains that the two characters are
different and distinct. The Jaina differs from them all and
maintains that universal and the particular are only
distinguishable traits in a real, which is at once identical with
and different from both." (JPN p.13)

It is, however, necessary to notice that :

"There is a difference - and intrinsic difference at that
- between a manifested and an unmanifested real. They are
identical and different both - identical in so far as it is the
same substance and different in so far as it undergoes a change
of characteristic. This is the Jaina position of
non-absolutism." (JPN, p.39.)

"A real is not entirely expressible in all its aspects
and modes. But it is not inexpressible altogether. A real being a
multiple entity is expressible and inexpressible both in
reference to different aspects; it is expressible in so far as it
partakes of a universal and is inexpressible so far as it is a
unique individual."3 (JPN., p. 113.)

"The unique individuality of a real is not accessible to
conceptual thought and, hence, to language, but it is reached by
an analysis of the nature of reality as it is apprehended in
perception; we have tried to prove, following the guidance of the
Jaina philosophers, that the nature of reals, on analysis, has
been found to exhibit the following traits, viz., existence,
non-existence and inexpressibility." (JPN, 127.)